Production-process modelling based on production-management data: a Petri-net approach
Summary (3 min read)
1. Introduction
- As the role played by information systems in production control increases, the need for a proper evaluation of the various decisions in both the design and operational stages of such systems is becoming more and more important.
- In section 3 the method for modelling the production system using data from the production-management system is presented.
2. Timed Petri nets
- Petri nets are a graphical and mathematical modelling tool that can be used to study systems that are characterized as being concurrent and asynchronous.
- A situation where conflict and concurrency are mixed is called a confusion.
- With enabling durations the firing of the transitions happens immediately and the time delays are represented by forcing transitions that are enabled to stay so for a specified period of time before they can fire.
- By using holding durations the formal representation of the timed Petri net is extended with the information of time, represented by the multiple TPN ¼ ðP;T; I;O; s0; fÞ; where P, T, I, O are the same as above, s0 is the initial state of the timed Petri net, and f : T !.
3. The modelling of production systems
- This section deals with models for production facilities.
- These models play a role in the design and the operational control of a plant.
- If used in all stages, an additional benefit of improving the communication between these stages is achieved.
- And the structure of the model is derived from existing production-management data (Wortmann 1995).
- A method for recognizing basic production elements from the management system’s database is provided.
3.1. The class of production system
- With the method presented here, several scheduling problems that appear in production systems can be solved.
- Different jobs are needed to produce a desired product.
- Each resource can process a limited number of operations.
- This limitation is defined by the capacity of resources. .
- Work orders define the quantity of desired products and the starting times.
3.2. The modelling of production activities
- First, a method of describing the production-system activities with timed Petri nets using the holding-duration representation of time is presented.
- When the resource is used at the start of the operation the unavailable token appears in place p1op.
- A particular operation can often be performed on different (sets of) resources with different availability, and the time duration can be different on each set of resources.
- If the operation chooses resource R3, its time duration is determined by the transition t2in¼ td2.
- An example of two successive operations is shown in figure 6, depicted as Op1 and Op2.
3.3. Modelling using the data from production-management systems
- The most widely used production-management information system in practice is MRP II.
- Table 1 shows an example of a BOM describing the production of product I, which is composed of two components, i.e. three items of J and and two items of K.
- The PN structure in figure 9 is achieved if the sequence of operations described by the routing table (table 2) is modelled.
- The procedure of each simulation step computes a new state skþ1¼ (mkþ1, nkþ1, rkþ1) of a timed Petri net in the next calculation interval.
- In the next stage the clocks for each token have to be determined rkþ1(pi).
5. Case study: the production of furniture fittings
- The applicability of their approach will be demonstrated on a model of a production system where furniture fittings are produced.
- The production system is divided into a number of departments.
- To implement a detailed schedule, how the work should be done, an additional scheduling system should be implemented.
- The process under consideration is an assembly process where different finished products are assembled from a number of sub-items.
- A description of the data presented in the table will be given later during the modelling procedure.
5.1. Modelling
- Data from the BOM and the routings were used to build a Petri-net model.
- As the authors can see from table 3, there are two work orders: the first has to start immediately with its production, while the starting time of the second is 80 time units later.
- The first operation in this table (Op1) shows that the sub-items should be produced first as prescribed by ‘BOM_CCL’.
- There is one operation needed to produce the subitem ‘Screw’, two operations to produce ‘Nut’ and ‘Clamp’, and three operations to produce the ‘Angle-bar with holder L’.
- Finally, the resulting model is verified using P-invariant analysis.
5.2. Results
- The scheduling problem was mapped onto timed Petri nets, and the assembly process was modelled with timed Petri nets.
- The authors tested different priority rules (SPT, LPT, etc.) and different schedules were achieved.
- It respects all the production constraints and the duration of the whole process can be identified.
- The PN-based heuristic search method of Lee and DiCesare (1994) was programmed in Matlab and used with a slightly modified heuristic function, as proposed by Yu et al. (2003b): hðmÞ ¼ w0 Op depthðmÞ.
- The result using this tool is presented in figure 18.
6. Conclusion
- To be able to analyse a production system, a mathematical model of the system is required.
- The production data are given with the BOM and the routings.
- For the particular timed Petri net the authors present a simulator that can be used to simulate models built with timed Petri nets.
- The applicability of the proposed approach was illustrated for an assembly process for producing furniture fittings.
- The model developed with the proposed method was used to determine a schedule for production operations.
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"Production-process modelling based ..." refers methods in this paper
...…rules is that they can easily be used in conjunction with production models derived within different mathematical modelling frameworks, e.g. the disjunctive graph model (Bła_zewicz et al. 1996, 2000), timed automata (Abdeddaim et al. 2006), and Petri nets (Murata 1989, Zhou and Venkatesh 1999)....
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"Production-process modelling based ..." refers background in this paper
...Instead, heuristic dispatching rules (Panwalker and Iskaneder 1977, Blackstone et al. 1982), such as Shortest Processing Time (SPT) or Longest Processing Time (LPT), are commonly used in practice....
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Frequently Asked Questions (15)
Q2. What are the future works in "Production-process modelling based on production-management data: a petri-net approach" ?
For future work the authors plan to investigate the applicability of highlevel Petri nets to the proposed modelling method as well as the use of the generated models for the testing of various heuristic search algorithms.
Q3. What is the use of timed Petri nets?
In their work, timed Petri nets with the holding-duration principle of time implementation were used to automate the modelling of a type of production system described by data from production-management systems.
Q4. What other methods have been used by other researchers?
The product structure given in the form of the BOM and the process structure in the form of routings have also been used by other researchers.
Q5. What are the main characteristics of soft-computing approaches?
Soft-computing approaches, e.g. genetic algorithms and neural networks, require considerable computation and only yield sub-optimal solutions.
Q6. What are the invariants that result from every distinguishable product route?
Seven of them are related to resources, two invariants refer to the precedence constraints and there are 14 invariants that result from every distinguishable product route.
Q7. What is the number of invariants in a Petri-net model?
So the number of invariants is defined by the sum of resources, the number of product routes and the number of precedences that are present in the model.
Q8. Why do the authors prefer the use of holding durations?
The authors prefer the use of holding durations, because in comparison with firing durations they do not have transitions that remain active over periods of time.
Q9. What is the way to use heuristic dispatching rules?
An interesting property of heuristic dispatching rules is that they can easily be used in conjunction with production models derived within different mathematical modelling frameworks, e.g. the disjunctive graph model (Bła_zewicz et al. 1996, 2000), timed automata (Abdeddaim et al. 2006), and Petri nets (Murata 1989, Zhou and Venkatesh 1999).
Q10. How does the firing duration principle work?
With enabling durations the firing of the transitions happens immediately and the time delays arerepresented by forcing transitions that are enabled to stay so for a specified period of time before they can fire.
Q11. What is the use of the same timed Petri net model?
The same timed Petri-net model can also be used in conjunction with other Petri-net scheduling algorithms, e.g. heuristic search.
Q12. What is the weighted sum of tokens that belongs to every shared resource?
It can be stated that the weighted sum of tokens that belongs to every P-invariant, which is a consequence of a resource, is equal to the capacity of that resource.
Q13. What is the function that is used to create the corresponding sequence of operations?
From the routing table the function yields the corresponding sequence of production operations and for each operation build a timed Petri net as defined in section 3.2.
Q14. What is the role of information systems in production control?
As the role played by information systems in production control increases, the need for a proper evaluation of the various decisions in both the design and operational stages of such systems is becoming more and more important.
Q15. What are the three basic ways of representing time in Petri nets?
As described by Bowden (2000) there are three basic ways of representing time in Petri nets: firing durations, holding durations and enabling durations.